The coalition government was today seeking a compromise over plans to make higher earning graduates pay more for their degrees as a Tory minister confirmed that a variable interest rate on student loans was a favoured option.

A review of higher education funding due out this week is expected to recommend that universities should be allowed to charge higher tuition fees and that the interest rate on student loans should increase.

Reports today suggested the review by Lord Browne would recommend abolishing the cap on fees, currently set at £3,290, and allowing the market to decide the cost of a degree.

The prospect of unlimited fees creates a huge dilemma for Lib Dem MPs who have signed a pledge both before and since the election to oppose any increase in fees. In a sign of Lib Dem nerves, senior staff ordered all the party's MPs not to speak to the press about fees, and instead wait until they had been briefed by Vince Cable, the business secretary.

At the weekend, in a message to his party's MPs, Cable ruled out a "pure graduate tax", saying it was unfair that higher earners should have to pay back many times the cost of their degree.

Transport secretary Philip Hammond, who was previously shadow chief secretary to the Treasury, said that a variable interest rate would allow the most high-flying graduates to subsidise the rest.

He told BBC1's Andrew Marr show: "There is a world of difference between a graduate tax, where people simply, because they have gone through university and used the student loan facility to do so, for the rest of their lives are being asked to pay a higher tax rate, and a variable interest rate on student loans where people who have borrowed money have the interest varied so that those with the lowest incomes have their interest rate effectively subsidised while those on the highest incomes provide something additional, to provide that subsidy."

He said that Cable had made "the right call" in deciding that a graduate tax would be unfair and unworkable.

The Tory minister insisted that any solution would have to be progressive, and transfer the burden from the taxpayer to better-off graduates.

"We can't go on, as we have done in the past, taxing people on low incomes in order for the taxpayer to meet the greater share of the burden of financing higher education," he said.

"It is right that those who benefit from high education make a contribution to it and it is right that those who benefit the most by going into very high paid work contribute the most."

The National Union of Students said last night it is an "insult to the intelligence" to try to "re-brand" an increase in fees as "progressive". Chair of Liberal Youth Martin Shapland said last night: "Until Lord Browne has submitted his report, all options should be considered. That said, Liberal Youth will not accept any rise in tuition fees. We urge our ministers and MPS to do the same."

Nick Clegg said in April that increasing tuition fees would be a "disaster".

The Lib Dems, who campaigned during the general election to scrap tuition fees, reaffirmed their commitment to replacing tuition fees and loans with a graduate tax at their party conference last month.

Aaron Porter, president of the NUS, said: "Vince Cable has gone out on a limb, arguing that they need to do something more progressive than a graduate tax. I don't know how that's possible with market-based fees.

"There can be nothing progressive about £7,000 fees. If the Liberal Democrats seek to betray students, frankly having deceived them at the time of the general election, we will take action against every MP."

As well as holding MPs to account at the ballot box, the NUS plans to campaign in each constituency to remind Lib Dem MPs of their pledge.

Shadow education secretary Andy Burnham warned that removing the tuition fees cap risked deterring poorer children from applying to the most prestigious universities.

Burnham told the BBC: "I worry greatly that we may be about to build a university system that is out of reach for ordinary families."

Ed Miliband, the Labour leader, rreiterated his support for a graduate tax to replace fees, and tried ot stoke a Liberal Democrat rebellion by promising to work with progressive forces in parliament to stop a big rise in tuition fees. It is feasible the Conservatives could be defeated on the issue since some Tories also oppose a graduated contributions for richer students in the form of higher interest rates on loans.

The Russell Group of universities, which includes Oxford and Cambridge, are keen for universities to be able to set their own fees.

But outside this elite, many universities will struggle to charge fees high enough to cover the costs of courses if government funding is cut in the spending review.

Students from ethnic minorities would be disproportionately affected by a two-tier university system. London Metropolitan University accepted 6,115 black students in 2007-08 – almost as many as the 7,815 black students spread among all 20 universities in the Russell Group.

A poll published yesterday showed that the graduate tax proposal had the backing of a majority of voters.

An ICM survey for The Sunday Telegraph found that 61% supported a graduate tax, compared with 29% who would rather see higher tuition fees.

Speaking at the Conservative party's conference last week, universities minister David Willetts made clear his opposition to a pure graduate tax.

Willetts said it was vital to maintain a connection between an individual and the university he or she attends: "so people can see that the money they pay in a graduate contribution is somehow linked to the university they went to, and one of the disadvantages of a full-blown graduate tax is that it weakens that link."

One way out of the coalition's difficulties is proposed in a research paper published today by the thinktank Policy Exchange. In it, Nick Barr, professor of public economics at the LSE, outlines a graduate contribution based on higher earners making extra repayments for up to a year. The extra cash could be limited to a maximum of 120% of the original loan in present value terms, the research suggests.

The paper says that loans for fees and for living expenses could be split, with a higher repayment threshold for the fees loans. That would mean no graduate earning less than £30,000 would be asked to repay the cost of tuition.

Professor Barr writes: "Low earners are entirely unaffected: the higher interest rate has no impact on monthly repayments, protecting people with low monthly earnings; and people with low lifetime earnings qualify for forgiveness after 25 years.

"The extra years are at the end of the repayment period, when a person's earnings are typically considerably higher than earlier in his or her career."